Noncommutative inspired Schwarzschild black hole, Voros product and Komar energy

Abstract

The importance of the Voros product in defining a noncommutative Schwarzschild black hole is shown. The entropy is then computed and the area law is shown to hold upto order $\frac{1}{\sqrt{\theta}}e^{-M^2/\theta}$. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy $E$ for these black holes is then obtained and a deformation from the conventional identity $E=2ST_H$ is found at the order $\sqrt{\theta}e^{-M^2/\theta}$. This deformation leads to a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. Finally, the Smarr formula is worked out. Similar features also exist for a deSitter-Schwarzschild geometry. This presentation is based on the work in references [1,2].